This paper presents a finite-element analysis for the cylindrical rods oscillating periodically in an incompressible viscous fluid. A system of discretized equation is obtained from the appropriate Navier-Stokes and continuity equations through Galerkin’s process. The basic unknowns are velocity and pressure. A mixed interpolation method is used. The added mass and viscous damping coefficients which characterize the fluid reaction force due to the rods oscillation can be obtained through a line integration of stress and pressure around the circumference of the rods. For the special case of a cylindrical rod oscillating in a viscous fluid enclosed by a rigid, concentric cylindrical shell, the finite-element solution agrees well with the analytical closed-form solution, which, in turn, has been verified experimentally [1].